3. Assume that Matts utility from consuming good X and good Y is given by the following function: U = 4X0.75Y0.25 Assume the price of X (PX) is 15, the price of Y (PY) is 10 and he has a budget of 1000 to spend on the two goods.

a. Using the Lagrangian multiplier, calculate Matts optimal consumption bundle. (You must clearly show all your working to receive the marks for this question).

b. Calculate Roberts level of utility as his optimal consumption point. (You must clearly show all your working to receive the marks for this question).

c. Calculate at Roberts optimal consumption point and provide an economic interpretation of its value. (You must clearly show all your working to receive the marks for this question).

d. Illustrate your answers to all the previous parts to this question on a clearly drawn and labelled indifference curve diagram. In particular, clearly and explain.

- The intercepts and slope of the budget constraint

- The optimum consumption combination.

- The quantity of both goods

- The level of utility at the optimum consumption bundle